A class of constacyclic codes over a finite field

Let Fq be a finite field with q=pm elements, where p is an odd prime and m⩾1. In this paper, we explicitly determine all the μ-constacyclic codes of length n2 over Fq, when the order of μ is a power of 2. We further obtain all the self-dual negacyclic codes of length n2 over Fq and give some illustrative examples. All the repeated-root λ-constacyclic codes of length n2ps over Fq are also determined for any nonzero λ in Fq. As examples all the 2-constacyclic, 3-constacyclic codes of length n2s5 over F5 and all the 3-constacyclic, 5-constacyclic codes of length n2s7 over F7 for n⩾1, s⩾1 are derived.